9.2.4: Geometry: Analyze characteristics of geometric shapes to make mathematical arguments and justifications about geometric relationships. Use visualization and geometric modeling to compare, solve problems and communicate ideas.

Geometry: Analyze characteristics of geometric shapes to make mathematical arguments and justifications about geometric relationships. Use visualization and geometric modeling to compare, solve problems and communicate ideas.

9.2.4.01Apply properties of angles, including corresponding, exterior, interior, vertical, complementary and supplementary angles, to solve situations and logically justify results. (MP1, MP3)9.2.4.02Apply properties of equilateral, isosceles and scalene triangles to solve situations and logically justify results. (MP1, MP3)9.2.4.03Apply properties such as interior and exterior angles and parallel and perpendicular sides to define, classify and solve situations involving regular and irregular polygons. (MP1)9.2.4.04Apply properties of congruent figures to solve situations and logically justify results. (MP1, MP3)9.2.4.05Accurately interpret and use words and phrases such as "if ... then," "if and only if," "all" and "not." Recognize the logical relationships between an "if ... then" statement and its inverse, converse and contrapositive. (MP6, MP7)9.2.4.06Analyze the validity of a logical argument and give counterexamples to disprove a statement. (MP1, MP3)9.2.4.07Construct logical arguments using axioms, definitions, theorems and postulates that clearly justify the reasoning. (MP3, MP6)9.2.4.08Identify, describe and solve situations using relationships among inscribed angles, circumscribed angles, radii and chords in circles. (MP5)9.2.4.09Describe and solve situations using the relationships of angles formed outside the circle for both secants and tangent lines. (MP7)9.2.4.10Apply properties of similar figures to solve situations and logically justify results. (MP3)9.2.4.11Show that two triangles are similar using the AA, SAS and SSS similarity criteria. (MP7)9.2.4.12Make geometric constructions with a variety of tools, including dynamic geometric technology, to examine theorems, make and test conjectures, represent transformations and develop mathematical reasoning skills in multi-step situations. (MP5)9.2.4.13Create and compare rigid and non-rigid transformations, and connect the preimage and image to congruence. (MP2)9.2.4.14Describe the steps used to show various sequences of transformations, applying reflections, rotations, translations and/or dilations of geometric figures that map one figure onto the other. (MP8)9.2.4.15Apply geometric methods to solve design situations, including designing an object or structure to satisfy physical constraints or optimize resources. (MP4)9.2.4.16Apply concepts of density based on area and volume in modeling contextual situations, including population density, BTUs per cubic foot and data storage. (MP4)

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